Results for 'Diagrammatic reasoning'

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  1.  63
    The Forgotten Individual: Diagrammatic Reasoning in Mathematics.Sun-Joo Shin - 2012 - Synthese 186 (1):149-168.
    Parallelism has been drawn between modes of representation and problem-sloving processes: Diagrams are more useful for brainstorming while symbolic representation is more welcomed in a formal proof. The paper gets to the root of this clear-cut dualistic picture and argues that the strength of diagrammatic reasoning in the brainstorming process does not have to be abandoned at the stage of proof, but instead should be appreciated and could be preserved in mathematical proofs.
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  2.  27
    An Eye-Tracking Study of Exploitations of Spatial Constraints in Diagrammatic Reasoning.Atsushi Shimojima & Yasuhiro Katagiri - 2013 - Cognitive Science 37 (2):211-254.
    Semantic studies on diagrammatic notations (Barwise & Etchemendy, ; Shimojima, ; Stenning & Lemon, ) have revealed that the “non-deductive,” “emergent,” or “perceptual” effects of diagrams (Chandrasekaran, Kurup, Banerjee, Josephson, & Winkler, ; Kulpa, ; Larkin & Simon, ; Lindsay, ) are all rooted in the exploitation of spatial constraints on graphical structures. Thus, theoretically, this process is a key factor in inference with diagrams, explaining the frequently observed reduction of inferential load. The purpose of this study was to (...)
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  3.  58
    Main Problems of Diagrammatic Reasoning. Part I: The Generalization Problem. [REVIEW]Zenon Kulpa - 2009 - Foundations of Science 14 (1-2):75-96.
    The paper attempts to analyze in some detail the main problems encountered in reasoning using diagrams, which may cause errors in reasoning, produce doubts concerning the reliability of diagrams, and impressions that diagrammatic reasoning lacks the rigour necessary for mathematical reasoning. The paper first argues that such impressions come from long neglect which led to a lack of well-developed, properly tested and reliable reasoning methods, as contrasted with the amount of work generations of mathematicians (...)
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  4.  65
    Human Diagrammatic Reasoning and Seeing-As.Annalisa Coliva - 2012 - Synthese 186 (1):121-148.
    The paper addresses the issue of human diagrammatic reasoning in the context of Euclidean geometry. It develops several philosophical categories which are useful for a description and an analysis of our experience while reasoning with diagrams. In particular, it draws the attention to the role of seeing-as; it analyzes its implications for proofs in Euclidean geometry and ventures the hypothesis that geometrical judgments are analytic and a priori, after all.
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  5.  59
    Renovating Philosophical Practice Through Diagrammatic Reasoning.Rocco Gangle - 2008 - Proceedings of the Xxii World Congress of Philosophy 4:47-52.
    The approach to the question of philosophical practice has been dominated by a subordination of practice to theory corresponding in general to a representational conception of philosophy. Methods of diagrammatic reasoning developed within philosophical semiotics provide a more effective approach. Inparticular, Peirce’s system of existential graphs exemplifies how diagrammatic reasoning is able formally to express the processes through which philosophical dialogue and cooperation actually take place and to link such processes to the methods and practices arising (...)
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  6.  36
    Theories of Diagrammatic Reasoning: Distinguishing Component Problems. [REVIEW]Corin Gurr, John Lee & Keith Stenning - 1998 - Minds and Machines 8 (4):533-557.
    Theories of diagrams and diagrammatic reasoning typically seek to account for either the formal semantics of diagrams, or for the advantages which diagrammatic representations hold for the reasoner over other forms of representation. Regrettably, almost no theory exists which accounts for both of these issues together, nor how they affect one another. We do not attempt to provide such an account here. We do, however, seek to lay out larger context than is generally used for examining the (...)
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  7.  41
    Prolegomena to a Cognitive Investigation of Euclidean Diagrammatic Reasoning.Yacin Hamami & John Mumma - 2013 - Journal of Logic, Language and Information 22 (4):421-448.
    Euclidean diagrammatic reasoning refers to the diagrammatic inferential practice that originated in the geometrical proofs of Euclid’s Elements. A seminal philosophical analysis of this practice by Manders (‘The Euclidean diagram’, 2008) has revealed that a systematic method of reasoning underlies the use of diagrams in Euclid’s proofs, leading in turn to a logical analysis aiming to capture this method formally via proof systems. The central premise of this paper is that our understanding of Euclidean diagrammatic (...)
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  8.  42
    Diagrammatic Reasoning and Modelling in the Imagination: The Secret Weapons of the Scientific Revolution.James Franklin - 2000 - In Guy Freeland & Anthony Corones (eds.), 1543 and All That: Image and Word, Change and Continuity in the Proto-Scientific Revolution. Kluwer Academic Publishers.
    Just before the Scientific Revolution, there was a "Mathematical Revolution", heavily based on geometrical and machine diagrams. The "faculty of imagination" (now called scientific visualization) was developed to allow 3D understanding of planetary motion, human anatomy and the workings of machines. 1543 saw the publication of the heavily geometrical work of Copernicus and Vesalius, as well as the first Italian translation of Euclid.
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  9.  64
    Diagrammatic Reasoning in Frege's Begriffsschrift.Danielle Macbeth - 2012 - Synthese 186 (1):289-314.
    In Part III of his 1879 logic Frege proves a theorem in the theory of sequences on the basis of four definitions. He claims in Grundlagen that this proof, despite being strictly deductive, constitutes a real extension of our knowledge, that it is ampliative rather than merely explicative. Frege furthermore connects this idea of ampliative deductive proof to what he thinks of as a fruitful definition, one that draws new lines. My aim is to show that we can make good (...)
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  10. Review of Macbeth, D. Diagrammatic Reasoning in Frege's Begriffsschrift. Synthese 186 (2012), No. 1, 289–314. Mathematical Reviews MR 2935338.John Corcoran - 2014 - MATHEMATICAL REVIEWS 2014:2935338.
    A Mathematical Review by John Corcoran, SUNY/Buffalo -/- Macbeth, Danielle Diagrammatic reasoning in Frege's Begriffsschrift. Synthese 186 (2012), no. 1, 289–314. ABSTRACT This review begins with two quotations from the paper: its abstract and the first paragraph of the conclusion. The point of the quotations is to make clear by the “give-them-enough-rope” strategy how murky, incompetent, and badly written the paper is. I know I am asking a lot, but I have to ask you to read the quoted (...)
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  11. Diagrammatic Reasoning as the Basis for Developing Concepts: A Semiotic Analysis of Students' Learning About Statistical Distribution.Arthur Bakker & Michael H. G. Hoffmann - 2005 - Educational Studies in Mathematics 60:333–358.
    In recent years, semiotics has become an innovative theoretical framework in mathematics education. The purpose of this article is to show that semiotics can be used to explain learning as a process of experimenting with and communicating about one's own representations of mathematical problems. As a paradigmatic example, we apply a Peircean semiotic framework to answer the question of how students learned the concept of "distribution" in a statistics course by "diagrammatic reasoning" and by developing "hypostatic abstractions," that (...)
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  12.  16
    Diagrammatic Reasoning: Some Notes on Charles S. Peirce and Friedrich A. Lange.Francesco Bellucci - 2013 - History and Philosophy of Logic 34 (4):293 - 305.
    According to the received view, Charles S. Peirce's theory of diagrammatic reasoning is derived from Kant's philosophy of mathematics. For Kant, only mathematics is constructive/synthetic, logic being instead discursive/analytic, while for Peirce, the entire domain of necessary reasoning, comprising mathematics and deductive logic, is diagrammatic, i.e. constructive in the Kantian sense. This shift was stimulated, as Peirce himself acknowledged, by the doctrines contained in Friedrich Albert Lange's Logische Studien (1877). The present paper reconstructs Peirce's reading of (...)
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  13.  5
    Cognitive Conditions of Diagrammatic Reasoning.Michael Hg Hoffmann - 2011 - Semiotica 2011 (186):189-212.
    In the first part of this paper, I delineate Peirce's general concept of diagrammatic reasoning from other usages of the term that focus either on diagrammatic systems as developed in logic and AI or on reasoning with mental models. The main function of Peirce's form of diagrammatic reasoning is to facilitate individual or social thinking processes in situations that are too complex to be coped with exclusively by internal cognitive means. I provide a (...) definition of diagrammatic reasoning that emphasizes the construction of, and experimentation with, external representations based on the rules and conventions of a chosen representation system. The second part starts with a summary of empirical research regarding cognitive effects of working with diagrams and a critique of approaches that use “mental models” to explain those effects. The main focus of this section is, however, to elaborate the idea that diagrammatic reasoning should be conceptualized as a case of “distributed cognition.” Using the mathematics lesson described by Plato in his Meno, I analyze those cognitive conditions of diagrammatic reasoning that are relevant in this case. (shrink)
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  14.  9
    Diagrammatic Reasoning: An Introduction.Riccardo Fusaroli & Kristian Tylén - 2014 - Pragmatics and Cognition 22 (2):183-186.
    Many types of everyday and specialized reasoning depend on diagrams: we use maps to fnd our way, we draw graphs and sketches to communicate concepts and prove geometrical theorems, and we manipulate diagrams to explore new creative solutions to problems. While the linear and symbolic character of verbal language has long served as the predominant model of human thought, it is remarkable how — through a range of contexts — thinking and communication critically depend on manipulations of external, ofen (...)
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  15.  10
    Space, Complementarity, and “Diagrammatic Reasoning”.Michael Otte - 2011 - Semiotica 2011 (186):275-296.
    In the development of pure mathematics during the nineteenth and twentieth centuries, two very different movements had prevailed. The so-called rigor movement of arithmetization, which turned into set theoretical foundationalism, on the one hand, and the axiomatic movement, which originated in Poncelet's or Peirce's emphasis on the continuity principle, on the other hand. Axiomatical mathematics or mathematics as diagrammatic reasoning represents a genetic perspective aiming at generalization, whereas mathematics as arithmetic or set theory is mainly concerned with foundation (...)
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  16.  31
    Aligning Logical and Psychological Perspectives on Diagrammatic Reasoning.Keith Stenning & Oliver Lemon - 2001 - Artificial Intelligence Review 15:29--62.
    We advance a theoretical framework which combines recent insights of research in logic, psychology, and formal semantics, on the nature of diagrammatic representation and reasoning. In particular, we wish to explain the varied efficacy of reasoning and representing with diagrams. In general we consider diagrammatic representations to be restricted in expressive power, and we wish to explain efficacy of reasoning with diagrams via the semantical and computational properties of such restricted `languages'. Connecting these foundational insights (...)
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  17.  89
    Hume on Space, Geometry, and Diagrammatic Reasoning.De Pierris Graciela - 2012 - Synthese 186 (1):169-189.
    Hume’s discussion of space, time, and mathematics at T 1.2 appeared to many earlier commentators as one of the weakest parts of his philosophy. From the point of view of pure mathematics, for example, Hume’s assumptions about the infinite may appear as crude misunderstandings of the continuum and infinite divisibility. I shall argue, on the contrary, that Hume’s views on this topic are deeply connected with his radically empiricist reliance on phenomenologically given sensory images. He insightfully shows that, working within (...)
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  18.  10
    Diagrammatic Reasoning: Abstraction, Interaction, and Insight.Kristian Tylén, Riccardo Fusaroli, Johanne Stege Bjørndahl, Joanna Raczaszek-Leonardi, Svend Østergaard & Frederik Stjernfelt - 2014 - Pragmatics and Cognition 22 (2):264-283.
    Many types of everyday and specialized reasoning depend on diagrams: we use maps to find our way, we draw graphs and sketches to communicate concepts and prove geometrical theorems, and we manipulate diagrams to explore new creative solutions to problems. The active involvement and manipulation of representational artifacts for purposes of thinking and communicating is discussed in relation to C.S. Peirce’s notion of diagrammatical reasoning. We propose to extend Peirce’s original ideas and sketch a conceptual framework that delineates (...)
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  19.  13
    Operational Constraints in Diagrammatic Reasoning.Atsushi Shimojima - 1996 - In Gerard Allwein & Jon Barwise (eds.), Logical Reasoning with Diagrams. Oxford University Press.
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  20.  27
    The Role of Diagrammatic Reasoning in Ethical Deliberation. Campos - 2015 - Transactions of the Charles S. Peirce Society 51 (3):338-357.
    In the 1903 lecture “What Makes a Reasoning Sound?” Charles Peirce provides a detailed account of the process of ethical deliberation intended to shape right conduct. He does this in the context of arguing against the claim that there is no distinction between moral right and wrong. He considered the argument for this claim to be analogous to the argument for the claim that there is no distinction between good and bad reasoning.1 Though Peirce’s ultimate concern in the (...)
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  21.  22
    Diagrammatic Reasoning.William Bechtel - unknown
    Diagrams figure prominently in human reasoning, especially in science. Cognitive science research has provided important insights into the inferences afforded by diagrams and revealed differences in the reasoning made possible by physically instantiated diagrams and merely imagined ones. In scientific practice, diagrams figures prominently both in the way scientists reason about data and in how they conceptualize explanatory mechanisms. To identify patterns in data, scientists often graph it. While some graph formats, such as line graphs, are used widely, (...)
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  22.  23
    The Role of Diagrammatic Reasoning in Ethical Deliberation. Campos - 2015 - Transactions of the Charles S. Peirce Society 51 (3):338.
    In the 1903 lecture “What Makes a Reasoning Sound?” Charles Peirce provides a detailed account of the process of ethical deliberation intended to shape right conduct. He does this in the context of arguing against the claim that there is no distinction between moral right and wrong. He considered the argument for this claim to be analogous to the argument for the claim that there is no distinction between good and bad reasoning.1 Though Peirce’s ultimate concern in the (...)
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  23.  1
    Inter-Diagrammatic Reasoning and Digital Geometry.Robert McCartney & Passent El-Kafrawy - 2004 - In A. Blackwell, K. Marriott & A. Shimojima (eds.), Diagrammatic Representation and Inference. Springer. pp. 199--215.
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  24.  51
    How to Get It. Diagrammatic Reasoning as a Tool of Knowledge Development and its Pragmatic Dimension.Michael H. G. Hoffmann - 2004 - Foundations of Science 9 (3):285-305.
    Discussions concerning belief revision, theorydevelopment, and ``creativity'' in philosophy andAI, reveal a growing interest in Peirce'sconcept of abduction. Peirce introducedabduction in an attempt to providetheoretical dignity and clarification to thedifficult problem of knowledge generation. Hewrote that ``An Abduction is Originary inrespect to being the only kind of argumentwhich starts a new idea'' (Peirce, CP 2.26).These discussions, however, led to considerabledebates about the precise way in which Peirce'sabduction can be used to explain knowledgegeneration (cf. Magnani, 1999; Hoffmann, 1999).The crucial question is (...)
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  25.  11
    Diagrammatic Reasoning in Euclid's Elements.Danielle Macbeth - 2010 - In Bart van Kerkhove, Jean Paul van Bendegem & Jonas de Vuyst (eds.), Philosophical Perspectives on Mathematical Practice 12. College Publications. pp. 235-267.
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  26.  10
    What is Diagrammatic Reasoning in Mathematics?Sochański Michał - forthcoming - Logic and Logical Philosophy.
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  27. Diagrammatic Reasoning and Representational Systems.Kenneth Manders - 2008 - In Paolo Mancosu (ed.), The Philosophy of Mathematical Practice. Oxford University Press.
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  28.  16
    Abstraction and Diagrammatic Reasoning in Aristotle’s Philosophy of Geometry.Justin Humphreys - 2017 - Apeiron 50 (2):197-224.
    Journal Name: Apeiron Issue: Ahead of print.
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  29.  32
    Diagrammatic Reasoning and Hypostatic Abstraction in Statistics Education.Arthur Bakker - 2007 - Semiotica 2007 (164):9-29.
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  30.  23
    Editorial: Efficacy of Diagrammatic Reasoning[REVIEW]Oliver Lemon, Maarten de Rijke & Atsushi Shimojima - 1999 - Journal of Logic, Language and Information 8 (3):265-271.
  31.  4
    Individuating in the Dark: Diagrammatic Reasoning and Attentional Shifts.Donna E. West - 2016 - Semiotica 2016 (210):35-56.
    Name der Zeitschrift: Semiotica Jahrgang: 2016 Heft: 210 Seiten: 35-56.
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  32. Peirce's "Diagrammatic Reasoning" as a Solution of the Learning Paradox.Michael H. G. Hoffmann - 2003 - In . Rodopi.
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  33. Signs as Means for Discoveries. Peirce and His Concepts of 'Diagrammatic Reasoning,' 'Theorematic Deduction,' 'Hypostatic Abstraction,' and 'Theoric Transformation'.Michael H. G. Hoffmann - 2005 - In . Springer.
    The paper aims to show how by elaborating the Peircean terms used in the title creativity in learning processes and in scientific discoveries can be explained within a semiotic framework. The essential idea is to emphasize both the role of external representations and of experimenting with those representations , and to describe a process consisting of three steps: First, looking at diagrams "from a novel point of view" offers opportunities to synthesize elements of these diagrams which have never been perceived (...)
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  34. Seeing Problems, Seeing Solutions. Abduction and Diagrammatic Reasoning in a Theory of Scientific Discovery.Michael H. G. Hoffmann - 2007 - In . Cfcul/Publidisa.
     
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  35.  41
    A Diagrammatic Inference System with Euler Circles.Koji Mineshima, Mitsuhiro Okada & Ryo Takemura - 2012 - Journal of Logic, Language and Information 21 (3):365-391.
    Proof-theory has traditionally been developed based on linguistic (symbolic) representations of logical proofs. Recently, however, logical reasoning based on diagrammatic or graphical representations has been investigated by logicians. Euler diagrams were introduced in the eighteenth century. But it is quite recent (more precisely, in the 1990s) that logicians started to study them from a formal logical viewpoint. We propose a novel approach to the formalization of Euler diagrammatic reasoning, in which diagrams are defined not in terms (...)
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  36. Augmenting Cognitive Architectures to Support Diagrammatic Imagination.Balakrishnan Chandrasekaran, Bonny Banerjee, Unmesh Kurup & Omkar Lele - 2011 - Topics in Cognitive Science 3 (4):760-777.
    Diagrams are a form of spatial representation that supports reasoning and problem solving. Even when diagrams are external, not to mention when there are no external representations, problem solving often calls for internal representations, that is, representations in cognition, of diagrammatic elements and internal perceptions on them. General cognitive architectures—Soar and ACT-R, to name the most prominent—do not have representations and operations to support diagrammatic reasoning. In this article, we examine some requirements for such internal representations (...)
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  37.  14
    Real Objects Can Impede Conditional Reasoning but Augmented Objects Do Not.Yuri Sato, Yutaro Sugimoto & Kazuhiro Ueda - 2018 - Cognitive Science 42 (2):691-707.
    In this study, Knauff and Johnson-Laird's visual impedance hypothesis is applied to the domain of external representations and diagrammatic reasoning. We show that the use of real objects and augmented real objects can control human interpretation and reasoning about conditionals. As participants made inferences, they also moved objects corresponding to premises. Participants who moved real objects made more invalid inferences than those who moved AR objects and those who did not manipulate objects. Our results showed that real (...)
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  38.  15
    On Automating Diagrammatic Proofs of Arithmetic Arguments.Mateja Jamnik, Alan Bundy & Ian Green - 1999 - Journal of Logic, Language and Information 8 (3):297-321.
    Theorems in automated theorem proving are usually proved by formal logical proofs. However, there is a subset of problems which humans can prove by the use of geometric operations on diagrams, so called diagrammatic proofs. Insight is often more clearly perceived in these proofs than in the corresponding algebraic proofs; they capture an intuitive notion of truthfulness that humans find easy to see and understand. We are investigating and automating such diagrammatic reasoning about mathematical theorems. Concrete, rather (...)
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  39.  39
    Proof Theory for Reasoning with Euler Diagrams: A Logic Translation and Normalization.Ryo Takemura - 2013 - Studia Logica 101 (1):157-191.
    Proof-theoretical notions and techniques, developed on the basis of sentential/symbolic representations of formal proofs, are applied to Euler diagrams. A translation of an Euler diagrammatic system into a natural deduction system is given, and the soundness and faithfulness of the translation are proved. Some consequences of the translation are discussed in view of the notion of free ride, which is mainly discussed in the literature of cognitive science as an account of inferential efficacy of diagrams. The translation enables us (...)
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  40.  17
    Where Syllogistic Reasoning Happens: An Argument for the Extended Mind Hypothesis.Georg Theiner - 2007 - In McNamara D. S. & Trafton J. G. (eds.), Proceedings of the 29th Annual Cognitive Science Society. Cognitive Science Society.
    Does cognition sometimes literally extend into the extra-organismic environment (Clark, 2003), or is it always “merely” environmentally embedded (Rupert, 2004)? Underlying this current border dispute is the question about how to individuate cognitive processes on principled grounds. Based on recent evidence about the active role of representation selection and construction in learning how to reason (Stenning, 2002), I raise the question: what makes two distinct, modality-specific pen-and-paper manipulations of external representations – diagrams versus sentences – cognitive processes of the same (...)
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  41.  11
    A Diagrammatic Representation for Entities and Mereotopological Relations in Ontologies.José M. Parente de Oliveira & Barry Smith - 2017 - In CEUR, vol. 1908.
    In the graphical representation of ontologies, it is customary to use graph theory as the representational background. We claim here that the standard graph-based approach has a number of limitations. We focus here on a problem in the graph-based representation of ontologies in complex domains such as biomedical, engineering and manufacturing: lack of mereotopological representation. Based on such limitation, we proposed a diagrammatic way to represent an entity’s structure and various forms of mereotopological relationships between the entities.
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  42.  55
    A Diagrammatic Reconstruction of Carnap's "Quasianalysis".Iulian D. Toader - 2004 - Synthese 142 (1):43-59.
    This paper criticizes two reconstructions of Carnap's technical procedure of quasianalysis, which were given by Nelson Goodman and Thomas Mormann. It then offers a diagrammatic reconstruction, one that does not ignore the essential role played by Lotze's concept of a local sign, and explains away a point raised by Quine against Carnap's project in the Aufbau.
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  43.  18
    The Sheet of Indication: A Diagrammatic Semantics for Peirce’s EG-Alpha.Gianluca Caterina & Rocco Gangle - 2015 - Synthese 192 (4):923-940.
    Following the guiding thread of Peirce’s use of diagrammatic syntax in his system of existential graphs , which depends crucially on the role of the Sheet of Assertion, we introduce the notion of Sheet of Indication as the basis for a general diagrammatic semantics applicable to a wide range of diagrams. We then show how Peirce’s EG-alpha graphs may be understood as instances of SIs and how logically coherent models of the graphs are represented in the SI semantics.
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  44. Kant on Geometry and Spatial Intuition.Michael Friedman - 2012 - Synthese 186 (1):231-255.
    I use recent work on Kant and diagrammatic reasoning to develop a reconsideration of central aspects of Kant’s philosophy of geometry and its relation to spatial intuition. In particular, I reconsider in this light the relations between geometrical concepts and their schemata, and the relationship between pure and empirical intuition. I argue that diagrammatic interpretations of Kant’s theory of geometrical intuition can, at best, capture only part of what Kant’s conception involves and that, for example, they cannot (...)
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  45. And so On...: Reasoning with Infinite Diagrams.Solomon Feferman - 2012 - Synthese 186 (1):371 - 386.
    This paper presents examples of infinite diagrams (as well as infinite limits of finite diagrams) whose use is more or less essential for understanding and accepting various proofs in higher mathematics. The significance of these is discussed with respect to the thesis that every proof can be formalized, and a "pre" form of this thesis that every proof can be presented in everyday statements-only form.
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  46.  38
    Introduction: Diagrammatical Reasoning and Peircean Logic Representations.João Queiroz & Frederik Stjernfelt - 2011 - Semiotica 2011 (186):1-4.
  47.  13
    Mapping Relational Structure in Spatial Reasoning.Merideth Gattis - 2004 - Cognitive Science 28 (4):589-610.
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  48.  28
    Syllogisms in Rudimentary Linear Logic, Diagrammatically.Ruggero Pagnan - 2013 - Journal of Logic, Language and Information 22 (1):71-113.
    We present a reading of the traditional syllogistics in a fragment of the propositional intuitionistic multiplicative linear logic and prove that with respect to a diagrammatic logical calculus that we introduced in a previous paper, a syllogism is provable in such a fragment if and only if it is diagrammatically provable. We extend this result to syllogistics with complemented terms à la De Morgan, with respect to a suitable extension of the diagrammatic reasoning system for the traditional (...)
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  49.  13
    Internal Diagrams and Archetypal Reasoning in Category Theory.Eduardo Ochs - 2013 - Logica Universalis 7 (3):291-321.
    We can regard operations that discard information, like specializing to a particular case or dropping the intermediate steps of a proof, as projections, and operations that reconstruct information as liftings. By working with several projections in parallel we can make sense of statements like “Set is the archetypal Cartesian Closed Category”, which means that proofs about CCCs can be done in the “archetypal language” and then lifted to proofs in the general setting. The method works even when our archetypal language (...)
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  50.  6
    From the Logical Square to Blanché's Hexagon: Formalization, Applicability and the Idea of the Normative Structure of Thought. [REVIEW]Aimable-André Dufatanye - 2012 - Logica Universalis 6 (1-2):45-67.
    The square of opposition and many other geometrical logical figures have increasingly proven to be applicable to different fields of knowledge. This paper seeks to show how Blanché generalizes the classical theory of oppositions of propositions and extends it to the structure of opposition of concepts. Furthermore, it considers how Blanché restructures the Apuleian square by transforming it into a hexagon. After presenting G. Kalinowski’s formalization of Blanché’s hexagonal theory, an illustration of its applicability to mathematics, to modal logic, and (...)
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